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Yes, it needs to be perpendicular to the direction of frankfurt for best results

You can find more details in the second page of this datasheet

https://www.gemischtwaren-haendler.de/shopdateien/3942_1.pdf

More importantly, you would need to know how the antenna is oriented within the enclosure of your clock. I'm pretty sure that that wasn't mentioned in the manual of the one I bought.

Most clocks are thin, so it's easier to guess the placement of the antenna.

Usually the antenna is parallel to the board - and the board is positioned in the largest dimension, which tends to be also parallel with the display.

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